图灵机算法

Question

Could you please help me? I need to write code for a one-tape Turing Machine that uses the following two-letter alphabet a and b.
So the programme should show the common prefix of the two words.
For example:
g(aab,aaaba) -> aa; g(_,abab) -> _; g(aaba,baa) -> _; g(_,_) -> _; g(babaab,babb) -> bab
Where g is the function of the Machine and underscore means an Empty word, between words we have space
I tried to implement the following option:
If at the start we see the letter a , then we erase it and move to the beginning of the second word. If we also see a letter a there, we erase it too and after both words we write a through a space. After that we return to the beginning of the first word and repeat this operation. When the first letter of the first word and the first letter of the second no longer match, we erase everything that is left. But I have some troubles with code, because after each operation a space between two words gets longer and I don't know how to control this. Also there is a trouble when the first or the second word is a common prefix fully, like this:
g(baa,baabab) -> baa

Answer 1

Your approach seems reasonable. From your description it sounds like you just have trouble generalizing some of the individual steps.

For instance, to deal with the growing spaces between the two words, remember that at any time in the program, the two words are separated by one or more spaces. So implement your seek operation for that general case.

For the common prefix case you have to deal with the situation that you eventually run out of characters to compare. So after deleting the character from the first word, while seeking for the beginning of the second word, check whether the first character you pass over is a letter or a space. If it's a space, you're in the prefix case and need to take care that you don't try to seek back to the first word later, because you already erased all of it and there's only spaces left. Similarly, if the second word is the prefix, you can detect this when seeking to the output.

Try breaking the algorithm down into its essential steps and test each of those steps in isolation. It is much easier to make sure you handle the corner cases correctly when you can focus on a simple step in isolation, instead of having to test it as part of the larger algorithm. Doing this is an essential skill in debugging code, so consider this a good exercise for that. Even if it seems painful at first, make sure you have a structured approach to analyzing problems and breaking your code down into smaller parts, and you will be able to fix any problems eventually. Happy coding!